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Integration by partial fraction problem (∫dx/x(x^2 + 4)^2)

  1. Feb 1, 2012 #1
    1. The problem statement, all variables and given/known data

    I came across a problem that I can't solve
    and it is ∫dx/x(x^2 + 4)^2

    2. Relevant equations

    None

    3. The attempt at a solution
    So I'm pretty sure this is to be solved by partial fraction since I am on a chapter on
    Integration by partial fraction.

    so I started with A/x + (Bx+C/x^2+4) + [Dx+E/(x^2 +4)^2]

    and I get a reeeeaallllyy loooonnngg equation once I go around that
    Am I on the right track? Or did I make a mistake? is this even to be solved by partial fraction?
     
  2. jcsd
  3. Feb 1, 2012 #2
    First rewrite as [itex]\int[/itex][itex]\frac{1}{x(x^2 + 4)^2}[/itex] dx

    Then turn into partial fractions (lets ignore the integral part for now and focus on the fraction): [itex]\frac{A}{x}[/itex] + [itex]\frac{B}{(x^2 + 4)^2}[/itex] = [itex]\frac{1}{x(x^2 + 4)^2}[/itex]

    A [itex](x^2 + 4)^2[/itex] + B[itex]x[/itex] = 1

    Solve for A and B and plug back in.
     
    Last edited: Feb 1, 2012
  4. Feb 1, 2012 #3

    SammyS

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    First try the substitution u = x2 .

    You will still get to work with partial fractions, but they won't be quite as complicated.

    I assume your problem is actually [itex]\displaystyle \int\ \frac{dx}{x(x^2+4)^2}\,.[/itex]

    Parentheses are important.
     
  5. Feb 1, 2012 #4

    vela

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    You should have written A/x + (Bx+C)/(x^2+4) + (Dx+E)/(x^2+4)^2. As SammyS said, parentheses are important.

    Your expansion is fine. If you stick with this approach, you should find A=1/16, B=-1/16, C=0, D=-1/4, and E=0.
     
  6. Feb 3, 2012 #5
    sorry for late response but thanks for the replies
     
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